Calculations
Chemistry requires you to know how to do certain calculations. These sheets
should help you with some of them…
Formula mass of any compound is found by adding together the relative
atomic masses of all the atoms in the molecule. (measured in atomic mass
units a.m.u.)
e.g.
NaOH
Element
Na
O
H
1
1
1
Relative atomic mass
23
16
1
X
X
X
40 a.m.u
One mole of a substance is its gram formula mass. This is the same as the
formula mass but uses grams as a unit.
So,
1 mole of NaOH is 40g
Mass / Number of moles calculations
We have established how to work out the formula mass and gram formula
mass of a substance.
Remember: 1 mole of a substance is the gram formula mass.
We can use the triangle below when carrying out calculations.
Mass
n
=
Number of moles
FM
=
Formula mass
M
=
mass
This tells us that:
n
FM
n
=
Mass
FM
FM
=
Mass
n
mass =
n
X
FM
Example 1:
Calculate the number of moles in 40g of sodium hydroxide (NaOH).
Mass =
Mass
n
FM
=
NaOH
FM
so, n =
40g
Element
Na
O
H
mass
FM
1
1
1
=
40
40
Atomic mass
X
23
X
16
X
1
=
40 a.m.u
=
1 mole
Example 2:
Calculate the number of moles in 79.75g of copper (II) sulphate (CuSO4).
Mass =
Mass
n
FM
=
CuSO4
FM
so, n =
79.75g
Element
Cu
S
O
mass
FM
Atomic mass
63.5 = 63.5
32.0 = 32.0
16.0 = 64.0
= 159.5 amu
1
1
4
X
X
X
=
79.75 =
159.5
0.5moles
Example 3:
Calculate the mass of 0.25 moles of sodium hydroxide (NaOH).
n
Mass
n
=
FM
=
NaOH
FM
so,
mass =
0.25 moles
Element
Na
O
H
1
1
1
Atomic mass
X
23
X
16
X
1
=
40 a.m.u
n X FM
= 0.25 X 40 =
10g
Concentrations
The concentration of a solution is measured in moles per litre
(sometimes written as mol l-1 )
mol / l
This means the number of moles of a solute dissolved in one litre of water
(the solvent).
Note:
Concentration is sometimes called molarity
1 molar solution =
1 mol / l
=
1 mol l-1
We can make a 1 mol / l solution by taking one mole of sodium hydroxide
and adding water until the total volume is one litre.
NaOH
FM
=
Element
Na
O
H
1
1
1
Atomic mass
X
23
X
16
X
1
=
40 a.m.u
1 mole of NaOH
=
gram formula mass
=
40g
40g of NaOH
+
enough water to 
make up to one litre
1 mol /l solution
of sodium hydroxide
(NaOH)
Volume / Concentration Calculations
If we need to work out a concentration or number of moles we have another
triangle we can use.
n
=
Number of moles
n
V
C
V
=
volume ( litres )
C
=
concentration (mol / l)
This tells us that:
n
=
V
V
=
n
c
C
=
n
V
X
C
Example 1
Calculate the number of moles of solute in 100cm3 of a 1.0 mol / l solution.
n
V
C
V
=
100cm3
C
=
1.0 mol / l
=
V
X
C
=
0.1
X
1.0
=
0.1 moles of solute
=
0.1 litres
so:
n
Example 2
Calculate the number of moles of solute in 500cm3 of a 0.2 mol / l solution.
n
V
C
V
=
500cm3
C
=
0.2 mol / l
=
V
X
C
=
0.5
X
0.2
=
0.1 moles of solute
=
0.5 litres
so:
n
Calculations using both formula
More difficult calculations require both triangles.
In preparing solutions of a certain
concentration we need to work out
how much solute is required.
Mass
n
n
FM
V
C
If you always use the same steps in the
same order, you will get the correct answer.
In your standard grade, a simple mistake in arithmetic can give you the wrong
answer, however clearly laid out working means the marker will only take
some marks from you.
Example 1
Calculate the mass of sodium hydroxide required to prepare 250cm3 of a
solution of concentration 0.1 mol / l
Step 1
What do you need to calculate?
Step 2
V
C
FM
What do you already know?
250cm3
=
0.25 litres
0.1 mol / l
Na
1
X
23
=
O
1
X
16
=
H
1
X
1
=
=
Step 3
Mass
? n  FM
=
=
=
Mass
23
16
1
40 amu
Look at the triangles, what do you need?
?
In order to work out mass
(Mass = n X FM)
you need to work out
number of moles
(n = V X C)
n
 V C
Step 4
n
=
=
=
V
X
C
0.25 X
0.1
0.025 moles
so,
mass =
=
=
n
X
0.025 X
0.1g
Answer: 0.1g of sodium hydroxide (NaOH) is required to prepare
250cm3 of a solution of concentration 0.1 mol / l.
FM
40
Example 2
What will be the concentration of 500 cm3 of solution containing 50 g of
sodium hydroxide (NaOH)
Step 1
What do you need to calculate?
Step 2
V
=
mass =
FM
=
What do you already know?
500cm3
=
0.5 litres
50g
Na
1
X
23
=
O
1
X
16
=
H
1
X
1
=
=
Step 3
Look at the triangles, what do you need?
 Mass
V
23
16
1
40 amu
In order to work out concentration
(C = n / V)
? n
? n  FM
Concentration
you need to work out number of moles
(n = mass / FM)
C
Step 4
n
=
mass =
FM
50
40
=
1.25 moles
C
=
n
v
1.25
0.5
=
2.5 mol /l
=
Answer: Concentration is 2.5 mol / l
(500cm3 solution
containing 50g
of NaOH)